CAJ | 학술논문

讨论具有一般线性耗散边界反馈的Euler-Bernoulli梁的指数镇定问题.首先将所讨论的系统化为抽象空间中的发展方程,并利用C0半群理论给出闭环系统解的存在唯一性.其次,对相应的闭环系统特征方程进行详尽的讨论计算,得到了系统本征值的分布特性,从而利用Lassel不变原理得到了闭环系统渐近稳定的充分必要条件.最后通过对闭环系统的本征值及其相应的本征函数进行估计,导出了相应的闭环系统指数稳定的充分必要条件.
토론구유일반선성모산변계반궤적Euler-Bernoulli량적지수진정문제.수선장소토론적계통화위추상공간중적발전방정,병이용C0반군이론급출폐배계통해적존재유일성.기차,대상응적폐배계통특정방정진행상진적토론계산,득도료계통본정치적분포특성,종이이용Lassel불변원리득도료폐배계통점근은정적충분필요조건.최후통과대폐배계통적본정치급기상응적본정함수진행고계,도출료상응적폐배계통지수은정적충분필요조건.
This paper studies the stabilization problem of Euler-Bernoulli beam with general dissipati ye boundary feedback controls. First, by virtue of semigroup theory, the considered system is converted into an evolution equation in abstract space and the uniqueness of the solution to the evolution equation is proved. Then the eigenvalues of the closed loop system is studied and the necessary and sufficient condition for the closed loop system to be asymptotically stable is derived.Finally, the condition for the closed loop system to be exponentially stable is worked out by estimating the corresponding eigenfunctions.